System and method for information protection

ABSTRACT

A computer-implemented method for information protection comprises: committing a transaction amount of a transaction with a first commitment scheme to obtain a transaction commitment value, committing a change of the transaction with a second commitment scheme to obtain a change commitment value, the first commitment scheme comprising a transaction blinding factor, and the second commitment scheme comprising a change blinding factor; encrypting a first combination of the change blinding factor and the change with a first key; transmitting the transaction blinding factor, the transaction amount, and the transaction commitment value to a recipient node associated with a recipient for the recipient node to verify the transaction; in response to that the recipient successfully verifies the transaction, obtaining an encrypted second combination of the transaction blinding factor and the transaction amount encrypted with a second key.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation application of the U.S. patent application Ser. No. 16/342,653 filed on Apr. 17, 2019 and entitled “SYSTEM AND METHOD FOR INFORMATION PROTECTION”, which is a national phase application of the International Application No. PCT/CN2018/117558, filed on Nov. 27, 2018. The contents of all of the above applications are incorporated by reference in the entirety.

TECHNICAL FIELD

This disclosure generally relates to methods and devices for information protection.

BACKGROUND

Privacy is important to communications and data transfers among various users. Without protection, the users are exposed to the risk of identity theft, illegal transfer, or other potential losses. The risk becomes even greater when the communications and transfers are implemented online, because of the free access of online information.

SUMMARY

Various embodiments of the present disclosure include systems, methods, and non-transitory computer readable media for information protection.

According to one aspect, a computer-implemented method for information protection comprises: committing a transaction amount t of a transaction with a first commitment scheme to obtain a transaction commitment value T, and committing a change y of the transaction with a second commitment scheme to obtain a change commitment value Y, the first commitment scheme comprising a transaction blinding factor r_(t), and the second commitment scheme comprising a change blinding factor r_(y); encrypting a first combination of the change blinding factor r_(y) and the change y with a first key KA; transmitting the transaction blinding factor r_(t), the transaction amount t, and the transaction commitment value T to a recipient node associated with a recipient of the transaction for the recipient node to verify the transaction; in response to that the recipient node successfully verifies the transaction, obtaining an encrypted second combination of the transaction blinding factor r_(t) and the transaction amount t encrypted with a second key KB; and transmitting the encrypted first combination and the encrypted second combination to a plurality of nodes in a blockchain for the nodes in the blockchain to verify the transaction.

In some embodiments, the first commitment scheme comprises a Pedersen commitment based at least on the transaction blinding factor r_(t) and with the transaction amount t being a corresponding committed value; and the second commitment scheme comprises a Pedersen commitment based at least on the change blinding factor r_(y) and with the change y being a corresponding committed value.

In some embodiments, transmitting the transaction blinding factor r_(t), the transaction amount t, and the transaction commitment value T to the recipient node associated with the recipient of the transaction for the recipient node to verify the transaction comprises: transmitting the transaction blinding factor r_(t), the transaction amount t, and the transaction commitment value T to the recipient node associated with the recipient of the transaction, causing the recipient node to verify if the transaction commitment value T is equal to the first commitment scheme committing the transaction amount t with the transaction blinding factor r_(t).

In some embodiments, obtaining the encrypted second combination comprises receiving from the recipient node the encrypted second combination and a signature SIGB associated with the encrypted second combination and the transaction commitment value T.

In some embodiments, the transaction amount t is tapped from one or more assets A₁, A₂, . . . , A_(k) of a sender of the transaction; each of the assets is associated with (1) a Pedersen commitment based at least on a blinding factor r_(ak) and a value of the each asset and (2) an encryption based at least on the blinding factor r_(ak) and the value of the each asset; and the change y is a difference between the transaction amount t and the tapped assets.

In some embodiments, before transmitting the encrypted first combination and the encrypted second combination to the plurality of nodes in the blockchain, the method further comprises: verifying the signature SIGB; and in response to successfully verifying the signature SIGB, generating a signature SIGA associated with the assets A₁, A₂, . . . , A_(k), the first combination, the second combination, the transaction commitment value T, the change commitment value Y, and a difference between a sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and a sum of the transaction blinding factor r_(t) and the change blinding factor r_(y).

In some embodiments, transmitting the encrypted first combination and the encrypted second combination to the plurality of nodes in the blockchain comprises: transmitting the assets A₁, A₂, . . . , A_(k), the first combination, the second combination, the transaction commitment value T, the change commitment value Y, a difference between a sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and a sum of the transaction blinding factor r_(t) and the change blinding factor r_(y), the signature SIGA, and the signature SIGB to the plurality of nodes in the blockchain.

In some embodiments, transmitting the encrypted first combination and the encrypted second combination to the plurality of nodes in the blockchain for the nodes in the blockchain to verify the transaction comprises: transmitting the encrypted first combination and the encrypted second combination to the plurality of nodes in the blockchain, causing the nodes in the blockchain to, in response to successfully verifying the transaction, issue the transaction amount t to the recipient, eliminate the assets A₁, A₂, . . . , A_(k), and issue the change y to the sender.

According to another aspect, a non-transitory computer-readable storage medium stores instructions that, when executed by a processor, cause the processor to perform operations comprising: committing a transaction amount t of a transaction with a first commitment scheme to obtain a transaction commitment value T, and committing a change y of the transaction with a second commitment scheme to obtain a change commitment value Y, the first commitment scheme comprising a transaction blinding factor r_(t), and the second commitment scheme comprising a change blinding factor r_(y); encrypting a first combination of the change blinding factor r_(y) and the change y with a first key KA; transmitting the transaction blinding factor r_(t), the transaction amount t, and the transaction commitment value T to a recipient node associated with a recipient of the transaction for the recipient node to verify the transaction; in response to that the recipient node successfully verifies the transaction, obtaining an encrypted second combination of the transaction blinding factor r_(t) and the transaction amount t encrypted with a second key KB; and transmitting the encrypted first combination and the encrypted second combination to a plurality of nodes in a blockchain for the nodes in the blockchain to verify the transaction.

According to another aspect, a system for information protection comprises a processor and a non-transitory computer-readable storage medium coupled to the processor, the storage medium storing instructions that, when executed by the processor, cause the system to perform operations comprising: committing a transaction amount t of a transaction with a first commitment scheme to obtain a transaction commitment value T, and committing a change y of the transaction with a second commitment scheme to obtain a change commitment value Y, the first commitment scheme comprising a transaction blinding factor r_(t), and the second commitment scheme comprising a change blinding factor r_(y); encrypting a first combination of the change blinding factor r_(y) and the change y with a first key KA; transmitting the transaction blinding factor r_(t), the transaction amount t, and the transaction commitment value T to a recipient node associated with a recipient of the transaction for the recipient node to verify the transaction; in response to that the recipient node successfully verifies the transaction, obtaining an encrypted second combination of the transaction blinding factor r_(t) and the transaction amount t encrypted with a second key KB; and transmitting the encrypted first combination and the encrypted second combination to a plurality of nodes in a blockchain for the nodes in the blockchain to verify the transaction.

According to another aspect, a computer-implemented method for information protection comprises: obtaining a transaction blinding factor r_(t), a transaction amount t of a transaction, and a transaction commitment value T from a sender node associated with a sender of a transaction, wherein: the transaction amount t is committed with a first commitment scheme to obtain the transaction commitment value T, the first commitment scheme comprising the transaction blinding factor r_(t); verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T; in response to successfully verifying the transaction, encrypting a second combination of the transaction blinding factor r_(t) and the transaction amount t with a second key KB; and transmitting the encrypted second combination to the sender node.

In some embodiments, verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T comprises verifying if the obtained transaction commitment value T is equal to the first commitment scheme committing the obtained transaction amount t with the obtained transaction blinding factor r_(t).

In some embodiments, before transmitting the encrypted second combination to the sender node, further comprising generating a signature SIGB associated with the encrypted second combination and the transaction commitment value T; and transmitting the encrypted second combination to the sender node comprises transmitting the encrypted second combination and the signature SIGB to the sender node.

According to another aspect, a non-transitory computer-readable storage medium stores instructions that, when executed by a processor, cause the processor to perform operations comprising: obtaining a transaction blinding factor r_(t), a transaction amount t of a transaction, and a transaction commitment value T from a sender node associated with a sender of a transaction, wherein: the transaction amount t is committed with a first commitment scheme to obtain the transaction commitment value T, the first commitment scheme comprising the transaction blinding factor r_(t); verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T; in response to successfully verifying the transaction, encrypting a second combination of the transaction blinding factor r_(t) and the transaction amount t with a second key KB; and transmitting the encrypted second combination to the sender node.

According to another aspect, a system for information protection comprises a processor and a non-transitory computer-readable storage medium coupled to the processor, the storage medium storing instructions that, when executed by the processor, cause the system to perform operations comprising: obtaining a transaction blinding factor r_(t), a transaction amount t of a transaction, and a transaction commitment value T from a sender node associated with a sender of a transaction, wherein: the transaction amount t is committed with a first commitment scheme to obtain the transaction commitment value T, the first commitment scheme comprising the transaction blinding factor r_(t); verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T; in response to successfully verifying the transaction, encrypting a second combination of the transaction blinding factor r_(t) and the transaction amount t with a second key KB; and transmitting the encrypted second combination to the sender node.

These and other features of the systems, methods, and non-transitory computer readable media disclosed herein, as well as the methods of operation and functions of the related elements of structure and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for purposes of illustration and description only and are not intended as a definition of the limits of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Certain features of various embodiments of the present technology are set forth with particularity in the appended claims. A better understanding of the features and advantages of the technology will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings of which:

FIG. 1 illustrates an exemplary system for information protection, in accordance with various embodiments.

FIG. 2 illustrates exemplary steps for transaction initiation and verification, in accordance with various embodiments.

FIG. 3 illustrates a flowchart of an exemplary method for information protection, in accordance with various embodiments.

FIG. 4 illustrates a flowchart of an exemplary method for information protection, in accordance with various embodiments.

FIG. 5 illustrates a block diagram of an exemplary computer system in which any of the embodiments described herein may be implemented.

DETAILED DESCRIPTION

Blockchain may be considered as a decentralized database, commonly referred to as a distributed ledger because the operation is performed by various nodes (e.g., computing devices) in a network. Any information may be written to the blockchain and saved or read from ft, Anyone may set up a server and join the blockchain network to become a node. Any node may contribute computing power to maintain the blockchain by performing complex computations, such as hash calculation to add a block to a current blockchain, and the added block may contain various types of data or information. The node that contributed the computing power for the added block may be rewarded with a token (e.g., digital currency unit). Since the blockchain has no central node, each node is equal and holds the entire blockchain database.

Nodes are, for example, computing devices or large computer systems that support the blockchain network and keep it running smoothly. There are two types of nodes, full nodes and lightweight nodes. Full nodes keep a complete copy of the blockchain. The full nodes on the blockchain network validate transactions and blocks they receive, and relay them to connected peers for providing consensus verification of the transactions. Lightweight nodes, on the other hand, only download a fraction of the blockchain. For example, lightweight nodes are used for digital currency transactions. A lightweight node will communicate to a full node when it wants to transact.

This decentralization property can help prevent the emergence of a management center in a controlled position. For example, the maintenance of the bitcoin blockchain is performed by the network of communication nodes of the bitcoin software in the running area. This disclosure uses one or more blockchains or digital currencies, such as bitcoin and Ethereum, as examples. A person with ordinary skill in the art should appreciate that the technical solutions disclosed in this disclosure can use or apply to other type of blockchains and digital currencies. That is, instead of banks, institutions, or administrators in the traditional sense, multiple intermediaries exist in a form of computer servers executing bitcoin software. These computer servers form a network connected via the Internet, wherein anyone can potentially join the network. Transactions accommodated by the network may be of a form: “user A wants to send Z bitcoins to user B,” wherein the transactions are broadcast to the network using readily available software applications. The computer servers function as bitcoin servers that are operable to validate these financial transactions, add a record of them to their copy of the ledger, and then broadcast these ledger additions to other servers of the network.

Maintaining the blockchain is referred to as “mining,” and those who do such maintenance are rewarded with newly created bitcoins and transaction fees as aforementioned. For example, nodes may determine if the transactions are valid based on a set of rules the blockchain network has agreed to. Miners may be located on any continent and process payments by verifying each transaction as valid and adding it to the blockchain. Such verification is achieved via consensus provided by a plurality of miners and assumes that there is no systematic collusion. In the end, all data will be consistent, because the computation has to meet certain requirements to be valid and all nodes will be synchronized to ensure that the blockchain is consistent. Thus, data can be consistently stored in a distributed system of blockchain nodes.

Through the mining process, transactions such as asset transfers are verified and added to a growing chain of blocks of a blockchain by network nodes. By traversing the entire blockchain, the verification may include, for example, whether the paying party has access to the transferring asset, whether the asset had been spent before, whether the transferring amount is correct, etc. For example, in a hypothetical transaction (e.g., a transaction of bitcoins under a UTXO (unspent transaction output) model, a transaction of Ethereum coins under an Account/Balance model) signed off by a sender, the proposed transaction may be broadcast to the blockchain network for mining. A miner needs to check if the transaction is eligible to be executed according to the blockchain history. If the sender's wallet balance has sufficient funds according to the existing blockchain history, the transaction is considered valid and can be added to the block. Once verified, the asset transfers may be included in the next block to be added to the blockchain.

A block is much like a database record. Each time writing data creates a block. These blocks are linked and protected using cryptography to become interconnected networks. Each block is connected to the previous block, which is also the origin of the name “blockchain.” Each block usually contains the cryptographic hash of the previous block, the generation time, and the actual data. For instance, each block contains two parts: a block header to record the feature value of the current block, and a body to record actual data (e.g., transaction data). The chain of blocks are linked via the block headers. Each block header may contain multiple feature values, such as version, previous block hash, merkle root, timestamp, difficulty target, and nonce. The previous block hash contains not only the address of the previous block, but also the hash of the data inside the previous block, thus making the blockchains immutable. The nonce is a number which, when included, yields a hash with a specified number of leading zero bits.

For mining, the hash of the contents of the new block is taken by a node. The nonce (e.g., random string) is appended to the hash to obtain a new string. The new string is hashed again. The final hash is then compared to the difficulty target (e.g., a level) and determined whether the final hash is actually less than the difficulty target or not. If not, then the nonce is changed and the process repeats again. If yes, then the block is added to the chain and the public ledger is updated and alerted of the addition. The node responsible for the successful addition is rewarded with bitcoins, for example, by adding a reward transaction to itself into the new block (known as coinbase generation).

That is, for every output “Y”, if k is chosen from a distribution with high min-entropy it is infeasible to find an input x such that H(k|x)=Y, where K is the nonce, x is the hash of the block, Y is the difficulty target, and “|” denotes concatenation. On account of cryptographic hashes being essentially random, in the sense that their output cannot be predicted from their inputs, there is only one known way to find the nonce: to try out integers one after the other, for example 1, then 2, then 3, and so on, which may be known as brute-force. The larger the number of leading zeros, the longer on average it will take to find a requisite nonce Y. In one example, the bitcoin system constantly adjusts the number of leading zeros, so that the average time to find a nonce is about ten minutes. That way, as processing capabilities of computing hardware increase with time, over the years, the bitcoin protocol will simply require more leading zero bits to make mining always take a duration of about ten minutes to implement.

As described, hashing is an important cornerstone for blockchain. The hash algorithm can be understood as a function that compresses messages of any length into a fixed-length message digest. More commonly used are MD5 and SHA. In some embodiments, the hash length of the blockchain is 256 bits, which means that no matter what the original content is, a 256-bit binary number is finally calculated. And it can be guaranteed that the corresponding hash is unique as long as the original content is different. For example, the hash of the string “123” is a8fdc205a9f19cc1c7507a60c4101b13d11d7fd0 (hexadecimal), which has 256 bits when converted to binary, and only “123” has this hash. The hash algorithm in the blockchain is irreversible, that is, the forward calculation is easy (from “123” to a8tdc205a9f19cc1c7507a60c4t01b1 c7507a60c4f01b13d11d7fd0), and the reverse calculation cannot be done even if all computing resources are exhausted. Thus, the hash of each block of the blockchain is unique.

Further, if the content of the block changes, its hash will change. The block and the hash are in one-to-one correspondence, and the hash of each block is specifically calculated for the block header. That is, the feature values of the block headers are connected to form a long string, and then the hash is calculated for the string. For example, “Hash=SHA256 (block header)” is a block hash calculation formula, SHA256 is a blockchain hash algorithm applied to block header. The hash is uniquely determined by the block header, and not the block body. As mentioned above, the block header contains a lot of content, including the hash of the current block, and the hash of the previous block. This means that if the contents of the current block change, or if the hash of the previous block changes, it will cause a hash change in the current block. If hacker modifies a block, the hash of that block changes. In order for a later block to connect to the modified block, the hacker must modify all subsequent blocks in turn, because the next block must contain the hash of the previous block. Otherwise the modified block will be detached from the blockchain. Due to design reasons, hash calculations are time-consuming, and it is almost impossible to modify multiple blocks in a short period of time unless the hacker has mastered more than 51% of the computing power of the entire network. Thus, the blockchain guarantees its own reliability, and once the data is written, it cannot be tampered with.

Once the miner finds the hash (that is, an eligible signature or solution) for the new block, the miner broadcasts this signature to all the other miners (nodes of the blockchain). Other miners now verify in their turn if that solution corresponds with the problem of the sender's block (that is, determine if the hash input actually results in that signature). If the solution is valid, the other miners will confirm the solution and agree that the new block can be added to the blockchain. Thus, the consensus of the new block is reached. This is also known as “proof of work.” The block for which consensus has been reached can now be added to the blockchain and is broadcast to all nodes on the network along with its signature. The nodes will accept the block and save it to their transaction data as long as the transactions inside the block correspond correctly with the current wallet balances (transaction history) at that point in time. Every time a new block gets added on top of this block, the addition also counts as another “confirmation” for the blocks before it. For example, if a transaction is included in block 502, and the blockchain is 507 blocks long, it means the transaction has five confirmations (corresponding to blocks 507 to 502). The more confirmations the transaction has, the harder it is for attackers to alter.

In some embodiments, an exemplary blockchain asset system utilizes public-key cryptography, in which two cryptographic keys, one public key and one private key, are generated. The public key can be thought of as being an account number, and the private key can be thought of as being ownership credentials. For example, a bitcoin wallet is a collection of the public and private keys. Ownership of an asset (e.g., digital currency, cash asset, stock, equity, bond) associated with a certain asset address can be demonstrated with knowledge of the private key belonging to the address. For example, bitcoin wallet software, sometimes referred as being “bitcoin client software”, allows a given user to transact bitcoins. A wallet program generates and stores private keys and communicates with peers on the bitcoin network.

In blockchain transactions, payers and payees are identified in the blockchain by their public cryptographic keys. For example, most contemporary bitcoin transfers are from one public key to a different public key. In practice hashes of these keys are used in the blockchain and are called “bitcoin addresses.” In principle, if a hypothetical attacker person S could steal money from person A by simply adding transactions to the blockchain ledger like “person A pays person S 100 bitcoins,” using the users' bitcoin addresses instead of their names. The bitcoin protocol prevents this kind of theft by requiring every transfer to be digitally signed with the payer's private key, and only signed transfers can be added to the blockchain ledger. Since person S cannot forge person A's signature, person S cannot defraud person A by adding an entry to the blockchain equivalent to “person A pays person S 200 bitcoins.” At the same time, anyone can verify person A's signature using his/her public key, and therefore that he/she has authorized any transaction in the blockchain where he/she is the payer.

In the bitcoin transaction context, to transfer some bitcoins to user B, user A may construct a record containing information about the transaction through a node. The record may be signed with user A's signing key (private key) and contains user A's public verification key and user B's public verification key. The signature is used to confirm that the transaction has come from the user, and also prevents the transaction from being altered by anyone once it has been issued. The record bundled with other record that took place in the same time window in a new block may be broadcast to the full nodes. Upon receiving the records, the full nodes may work on incorporating the records into the ledge of all transactions that have ever taken place in the blockchain system, adding the new block to a previously-accepted blockchain through the above-described mining process, and validate the added block against the network's consensus rules.

UTXO (unspent transaction output) model and Account/Balance model are two exemplary models for implementing blockchain transactions. UTXO is a blockchain object model. Under UTXO, assets are represented by outputs of blockchain transactions that have not been spent, which can be used as inputs in new transactions. For example, user A's asset to be transferred may be in a form of UTXO. To spend (transact) the asset, user A has to sign off with the private key. Bitcoin is an example of a digital currency that uses UTXO model. In the case of a valid blockchain transaction, unspent outputs may be used to effect further transactions. In some embodiments, only unspent outputs may be used in further transactions to prevent double spending and fraud. For this reason, inputs on a blockchain are deleted when a transaction occurs, whilst at the same time, outputs are created in the form of UTXOs. These unspent transaction outputs may be used (by the holders of private keys, for example, persons with digital currency wallets) for the purpose of future transactions.

Account/Balance Model (or referred to as Account-based Transaction Model), on the other hand, keeps track of the balance of each account as a global state. The balance of an account is checked to make sure it is larger than or equal to the spending transaction amount. An example of how Account/Balance Model works in Ethereum is provided:

1. Alice gains 5 ethers through mining. It is recorded in the system that Alice has 5 ethers.

2. Alice wants to give Bob 1 ether, so the system will first deduct 1 ether from Alice's account, so Alice now has 4 ethers.

3. The system then increases Bob's account by 1 ether. The system knows that Bob has 2 ethers to begin with, therefore Bob's balance is increased to 3 ethers.

The record-keeping for Ethereum may be like that in a bank. An analogy is using an ATM/debit card. The bank tracks how much money each debit card has, and when Bob needs to spend money, the bank checks its record to make sure Bob has enough balance before approving the transaction.

Since the blockchain and other similar ledgers are completely public, the blockchain itself has no privacy protection. The public nature of P2P network means that, while those who use it are not identified by name, linking transactions to individuals and companies is feasible. For example, in cross-border remittances or in the supply chain, transaction amount has an extremely high level of privacy protection value, because with the transaction amount information, it is possible to infer the specific location and identities of the transaction parties. The subject matter of the transaction may comprise, for example, money, token, digital currency, contract, deed, medical record, customer detail, stock, bond, equity, or any other asset that can be described in digital form. Though UTXO model may provide anonymity to transaction amounts, for example, through ring signature in Monero and zero-knowledge cryptography Zcash, transaction amounts remain unprotected under Account/Balance Model. Thus, a technical problem address by the present disclosure is how to protect online information such as the privacy of transaction amounts. Such transactions may be under Account/Balance Model.

Some existing technologies propose to use the Pedersen commitment scheme to encrypt the transaction amount and replace Account/Balance Model. Under the scheme, the sender sends the transaction amount and a random number corresponding to the Pedersen commitment of the transaction amount to the payee through a secured channel off the blockchain. The payee verifies if the random number matches the transaction commitment and performs local storage. For example, under Account/Balance Model, an account can be treated as a wallet (account) for keeping assets that are aggregated but not merged. Each asset may correspond to an asset type (e.g., cryptocurrency), and the balance of the account is the sum of the asset values. Even assets of the same type are not merged. During transaction, a recipient of a transferring asset may be specified, and corresponding asset may be removed from the wallet to fund the transaction. The blockchain nodes verify that the paying wallet has sufficient asset(s) to cover the transaction, and then the nodes delete the transferred asset from the paying wallet and add a corresponding asset to a recipient wallet.

However, limitations still exist for such scheme. The transaction amount and random number generated by Pedersen commitment are privacy-sensitive data, Parties other than those related to the transaction should not have the opportunity to know the values, Thus, such information should be encrypted and saved, and decrypted when used. The committed value and the random number are necessary elements for spending the transacted asset in a future time but are easy to lose and difficult to recover for a lack of safe, stable, and efficient way to properly store random numbers. For example, the scheme of current technologies requires the user to maintain a persistent storage locally to manage the random numbers and plaintext balances corresponding to the encrypted account balance, and the management implementation is complicated. Further, the storage of the blinding factors (e.g., the random numbers) and the plaintext balances corresponding to the “Pedersen asset” in a single local node is prone to loss or corruption, while multi-node backup storage is difficult to realize due to the frequent change of the account balance.

The systems and method presented in this disclosure may overcome the above limitations and achieve robust privacy protection for transaction amounts, asset values, and blinding factors in commitment schemes. To that end, various cryptographic information exchange protocols may be used to encrypt/decrypt the random numbers and the plaintext balances, thus providing convenient management. Further, storing the encrypted information in blockchain ensures that the transaction amounts, asset values, and blinding factors in commitment schemes are not easily lost or tampered with.

In some embodiments, a commitment scheme (e.g., Pedersen commitment) may encrypt certain value a (e.g., transaction amount, asset value, key parameter) as follows:

PC(a)=r×G+a×H

where r is a random blinding factor (alternatively referred to as binding factor) that provides hiding, G and H are the publicly agreed generators/basepoints of the elliptic curve and may be chosen randomly, sn is the value of the commitment, C(sn) is the curve point used as commitment and given to the counterparty, and H is another curve point. That is, G and H may be known parameters to nodes. A “nothing up my sleeve” generation of H may be generated by hashing the basepoint G with a hash function mapping from a point to another with H=Hash(G). H and G are the public parameters of the given system (e.g., randomly generated points on an elliptic curve). Although the above provides an example of Pedersen commitment in elliptic curve form, various other forms of Pedersen commitment or other commitment schemes may be alternatively used.

A commitment scheme maintains data secrecy but commits to the data so that it cannot be changed later by the sender of the data. If a party only knows the commitment value (e.g., PC(a)), they cannot determine what underlying data values (e.g., a) have been committing to. Both the data (e.g., a) and the blinding factor (e.g., r) may be revealed later (e.g., by the initiator node), and a recipient (e.g., consensus node) of the commitment can run the commitment and verify that the committed data matches the revealed data. The blinding factor is present because without one, someone could try guessing at the data.

Commitment schemes are a way for the sender (committing party) to commit to a value (e.g., a) such that the value committed remains private, but can be revealed at a later time when the committing party divulges a necessary parameter of the commitment process. Strong commitment schemes may be both information hiding and computationally binding. Hiding refers to the notion that a given value a and a commitment of that value PC(a) should be unrelatable. That is, PC(a) should reveal no information about a. With PC(a), G, and H known, it is almost impossible to know a because of the random number r. A commitment scheme is binding if there is no plausible way that two different values can result in the same commitment. A Pedersen commitment is perfectly hiding and computationally binding under the discrete logarithm assumption. Further, with r, G, H, and PC(a) known, it is possible to verify PC(a) by determining if PC(a)=r×G+a×H.

A Pedersen commitment has an additional property: commitments can be added, and the sum of a set of commitments is the same as a commitment to the sum of the data (with a blinding factor set as the sum of the blinding factors): PC(r₁, data₁)+PC(r₂, data₂)==PC(r₁+r₂, data₁+data₂); PC(r₁, data₁)−PC(r₁, data₁)==0. In other words, the commitment preserves addition and the commutative property applies, i.e., the Pedersen commitment is additively homomorphic, in that the underlying data may be manipulated mathematically as if it is not encrypted.

In one embodiment, a Pedersen commitment used to encrypt the input value may be constructed using elliptic curve points. Conventionally, an elliptic curve cryptography (ECC) pubkey is created by multiplying a generator for the group (G) with the secret key (r): Pub=rG. The result may be serialized as a 33-byte array. ECC public keys may obey the additively homomorphic property mentioned before with respect to Pedersen commitments. That is: Pub1+Pub2=(r1+r2(mod n))G.

The Pedersen commitment for the input value may be created by picking an additional generator for the group (H, in the equations below) such that no one knows the discrete log for second generator H with respect to first generator G (or vice versa), meaning no one knows an x such that xG=H. This may be accomplished, for example, by using the cryptographic hash of G to pick H: H=to_point(SHA256(ENCODE(G))).

Given the two generators G and H, an exemplary commitment scheme to encrypt the input value may be defined as: commitment=rG+aH. Here, r may be the secret blinding factor, and a may be the input value being committing to. Hence, if sn is committed, the above-described commitment scheme PC(a)=r×G+a×H can be obtained. The Pedersen commitments are information-theoretically private: for any commitment, there exists some blinding factor which would make any amount match the commitment. The Pedersen commitments may be computationally secure against fake commitment, in that the arbitrary mapping may not be computed.

The party (node) that committed the value may open the commitment by disclosing the original value a and the factor r that completes the commitment equation. The party wishing to open the value PC(a) will then compute the commitment again to verify that the original value shared indeed matches the commitment PC(a) initially received. Thus, the asset type information can be protected by mapping it to a unique serial number, and then encrypting it by Pedersen commitment. The random number r chosen when generating the commitment makes it almost impossible for anyone to infer the type of asset type that is committed according to the commitment value PC(a).

In some embodiments, various cryptographic information exchange protocols may be used, such as Public-key protocol, symmetric encryption protocol, Diffie-Hellman (DH) key exchange, etc. For example, DH key exchange may be used as a method for securely exchanging cryptographic keys over a public channel. DH key exchange, also called exponential key exchange, is a method of digital encryption that uses numbers raised to specific powers to produce decryption keys on the basis of components that are never directly transmitted, making the task of a would-be code breaker mathematically overwhelming.

In an example of implementing Diffie-Hellman (DH) key exchange, the two end users Alice and Bob, while communicating over a channel they know to be private, mutually agree on positive whole numbers p and q, such that p is a prime number and q is a generator of p. The generator q is a number that, when raised to positive whole-number powers less than p, never produces the same result for any two such whole numbers. The value of p may be large, but the value of q is usually small. That is, q is a primitive root modulus p.

Once Alice and Bob have agreed on p and q in private, they choose positive whole-number personal keys a and b, both less than the prime-number modulus p and both may be randomly generated. Neither user divulges their personal key to anyone, and ideally, they memorize these numbers and do not write them down or store them anywhere. Next, Alice and Bob compute public keys a* and b* based on their personal keys according to the formulas

a*=q^(a) mod p

and

b*=q^(b) mod p

The two users can share their public keys a* and b* over a communication medium assumed to be insecure, such as the Internet or a corporate wide area network (WAN). From these public keys, a number k1 can be generated by either user on the basis of their own personal keys.

Alice computes k1 using the formula: k1=(b*)^(a) mod p

Bob computes k1 using the formula: k1=(a*)^(b) mod p

The value of k1 turns out to be the same according to either of the above two formulas. However, the personal keys a and b, which are critical in the calculation of k1, have not been transmitted over a public medium. Even with p, q, a* and b*, it is still very difficult to calculate a and b. Because it is a large and apparently random number, a potential hacker has almost no chance of correctly guessing k1, even with the help of a powerful computer to conduct millions of trials. The two users can therefore, in theory, communicate privately over a public medium with an encryption method of their choice using the decryption key k1.

In another example of implementing Diffie-Hellman (DH) key exchange, all calculations happen in a discrete group of sufficient size, where the Diffie-Hellman problem is considered hard, usually the multiplicative group modulo a big prime (e.g., for classical DH) or an elliptic curve group (e.g., for Elliptic curve Diffie-Hellman).

For two parties, each party chooses a private key a or b. Each party calculates the corresponding public key aG or bG. Each party sends the public key aG or bG to the other party. Each party uses the received public key together with its own private key to calculate the new shared secret a(bG)=b(aG), which can then be used with a key derivation function to derive a set of keys for a symmetric encryption scheme. Alternatively, various other computation methods can be used, for example, by generating public keys g^(a) and g^(b) and shared key gab or g^(ba).

During transactions, information protection is important to secure user privacy, and transaction amount is one type of information that has lacked protection. FIG. 1 shows an exemplary system 100 for information protection, in accordance with various embodiments. As shown, a blockchain network may comprise a plurality of nodes (e.g., full nodes implemented in servers, computers, etc.). For some blockchain platform (e.g., NEO), full nodes with certain level of voting power may be referred to as consensus nodes, which assume the responsibility of transaction verification. In this disclosure, full nodes, consensus nodes, or other equivalent nodes can verify the transaction.

Also, as shown in FIG. 1, user A and user B may use corresponding devices, such as laptops and mobile phones serving as lightweight nodes to perform transactions. For example, user A may want to transact with user B by transferring some asset in user A's account to user B's account. User A and user B may use corresponding devices installed with an appropriate blockchain software for the transaction. User A's device may be referred to as an initiator node A that initiates a transaction with user B's device referred to as recipient node B. Node A may access the blockchain through communication with node 1, and Node B may access the blockchain through communication with node 2. For example, node A and node B may submit transactions to the blockchain through node 1 and node 2 to request adding the transactions to the blockchain. Off the blockchain, node A and node B may have other channels of communication (e.g., regular internet communication without going through nodes 1 and 2).

Each of the nodes in FIG. 1 may comprise a processor and a non-transitory computer-readable storage medium coupled to the processor, the storage medium storing instructions that, when executed by the processor, cause the node (e.g., the processor) to perform various steps for information protection described herein. The each node may be installed with a software (e.g., transaction program) and/or hardware (e.g., wires, wireless connections) to communicate with other nodes and/or other devices. Further details of the node hardware and software are described later with reference to FIG. 5.

FIG. 2 illustrates exemplary steps for transaction and verification among a sender node A, a recipient node B, and one or more verifying nodes, in accordance with various embodiments. The operations presented below are intended to be illustrative. Depending on the implementation, the exemplary steps may include additional, fewer, or alternative steps performed in various orders or in parallel.

In various embodiments, accounts of transaction parties (sender user A and recipient user B) are configured for Account/Balance model. User A and user B may perform the following steps to carry out the transaction via one or more devices, such as their laptop, mobile phone, etc. The devices may be installed with appropriated software and hardware to perform the various steps. Each account may be associated with a cryptographic private key (secret key)-public key pair. The private key may be denoted as SK, and the public key may be denoted as PK. The private key may be used to sign off transmitted information (e.g., transaction information). The public key may be used to verify the signed information and generate account address. Each account may contain various assets, each denoted as: (V=PC(r, v), E_(K)(r, v)), where v represents the face value of the asset, V represents a Pedersen commitment of the face value v, r is a blinding factor (e.g., a random number), PC( ) is a Pedersen commitment algorithm, E( ) is an encryption algorithm (e.g., cryptographic key encryption algorithm), and K is an encryption key that is unique to each account. For example, each asset can be denoted as (V=PC(r, v), E_(K)(r∥v)), where ∥ represents concatenation. Although concatenation is used in the following embodiments, other alternative representations that involve r and v may be used. The encryption key K (e.g., KA, KB) can be generated by various methods such as private key protocol, key derivation function, etc. Each asset may also include information other than that listed, such as the source information of the asset.

In one example, before user A successfully transacts an amount t to user B in a blockchain-verified transaction, the addresses of and assets in A's account and B's account are as follows:

-   -   For A's Account (account A):     -   Address: AddrA     -   Public Key: PK_(A)     -   Private Key: SK_(A)     -   First Key: KA     -   Assets A₁ to A_(m) respectively of values a₁ to a_(m) are         denoted as:

(A₁ = PC(r_(a 1), a₁), E_(KA)(r_(a 1), a₁)), (A₂ = PC(r_(a 2), a₂), E_(KA)(r_(a 2), a₂)), ⋯(A_(m) = PC(r_(a m), a_(m)), E_(KA)(r_(a m), a_(m)))

-   -   For B's Account (account B):     -   Address: AddrB     -   Public Key: PKB     -   Private Key: SKB     -   Second Key: KB     -   Assets B₁ to B_(n) respectively of values b₁ to b_(n) are         denoted as:

(B₁ = PC(r_(b 1), b₁), E_(KB)(r_(b 1), b₁)), (B₂ = PC(r_(b 2), b₂), E_(KB)(r_(b 2), b₂)), ⋯(B_(n) = PC(r_(bn), b_(n)), E_(KB)(r_(bn), b_(n)))

In some embodiments, at step 201, node A may initiate a transaction with node B. For example, user A and user B may negotiate a transaction amount t from user A's account A to user B's account B. Account A and account B may correspond to the “wallets” described herein. Account A may have one or more assets. The asset may comprise, for example, money, token, digital currency, contract, deed, medical record, customer detail, stock, bond, equity, or any other asset that can be described in digital form. Account B may have one or more assets or no asset. Each asset may be associated with various blockchain information stored in blocks of the blockchain, the blockchain information comprising, for example, NoteType representing asset type, NoteID representing unique identification of asset, commitment values representing a commitment (e.g., Pedersen commitment) value of the asset value, encryption of random number and asset value, etc.

As described with respect to account A, in some embodiments, assets A₁ to A_(m) respectively correspond to asset values a₁ to a_(m) and random numbers r_(a1) to r_(am). Based on the random numbers r_(a1) to r_(am), node A may commit the asset values in account A to a commitment scheme (e.g., Pedersen commitment) to obtain encrypted commitment values. For example, for account A, the encrypted commitment values may be PC₁ to PC_(m), where PC_(i)=PC(r_(ai), a_(i))=r_(ai)×G+a_(i)×H, G and H are known, and i is a variable between 1 and m. In addition to the first field PC( . . . ), each asset is also associated with a second field E( . . . ) as described earlier. The second field E( . . . ) may represent an encryption of the corresponding random number and asset value encrypted with key KA. For example, the encryption may be E_(KA)(r_(ai), a_(i)). The PC( . . . ) and E( . . . ) for each asset may be inherited from previous transactions. The same mechanism may apply to account B and its assets.

In some embodiments, to satisfy the transaction amount t, user A may use a first key KA (e.g., a symmetric encryption key) to decrypt one or more assets of an aggregated value at least t from account A. For example, node A may tap assets A₁, A₂, . . . , A_(k) for this transaction, where k is less than or equal to m. The remaining assets A_(k+1), A_(k+2), A_(m) of account A are untapped. Correspondingly, node A may read assets PC(r_(a1), a₁), PC(r_(a2), a₂), . . . , PC(r_(ak), a_(k)) from node 1. With the random numbers r_(a1), r_(a2), . . . , r_(ak) known to node A, node A can decrypt the read assets PC(r_(a1), a₁), PC(r_(a2), a₂), . . . , PC(r_(ak), a_(k)) to obtain asset values a₁, a₂, . . . , a_(k) to ensure that the sum (a₁+a₂+ . . . +a_(k)) is no less than the transaction amount t. Different assets may be exchanged to one another within the account based on various rates.

In some embodiments, the symmetric encryption key may refer to the same cryptographic keys used in the cryptographic symmetric-key algorithm for both encryption of plaintext and decryption of ciphertext. The keys may be identical or there may be a simple transformation to go between the two keys. The keys may represent a shared secret between two or more parties that can be used to maintain a private information link.

In some embodiments, the amount of selected asset value in excess of t, if any, is set toy as the change. For example, node A may determine the change y=(a₁+a₂+ . . . +a_(k))−t. Node A may select random numbers r_(t) and r_(y) as blinding factors to generate Pedersen commitments for t and y: T=PC(r_(t), t), Y=PC(r_(y), y). That is, node A may generate a random number r_(t) for t and a random number r_(y) for y. Node A can commit t and r_(t) to a commitment scheme (e.g., homomorphic encryption) to obtain commitment value T=PC(r_(t), t), and commit y and r_(y) to a commitment scheme (e.g., homomorphic encryption) to obtain commitment value Y=PC(r_(y), y). Further, node A may determine r′=(r₁+r₂ . . . +r_(k))−r_(t)−r_(y).

In some embodiments, node A may use the first key KA to encrypt(r_(y), y), obtaining encryption E_(KA)(r_(y), y). Node A may store E_(KA)(r_(y), y) locally.

At step 202, node A may send the transaction information to node B (e.g., through blockchain, through a secured channel off the blockchain). The sent transaction information may comprise, for example, the random number r_(t), the transaction amount t, and commitment value T. The transaction information may be sent in plaintext.

At step 203, node B may verify the random number r_(t), the transaction amount t, and the commitment value T. In some embodiments, node B may verify if the amount t to send to user B is correct, and if T=PC(r_(t), t). For step 203, if the match/verification fails, node B may reject the transaction. If the match/verification succeeds, node B may reply node A at step 204.

At step 204, node B may encrypt (r_(t), t) with a second key KB (e.g., a symmetric encryption key) to obtain encryption E_(KB)(r_(t), t) and sign the transaction (E_(KB)(r_(t), t), T) with user B's private key SK_(B) to generate a signature SIGB. The signing may follow Digital Signature Algorithm (DSA) such as Elliptic Curve Digital Signature Algorithm (ECDSA), whereby the receiver of the signature can verify the signature with the signator's public key to authenticate the signed data. The signature SIGB indicates that the recipient node B agrees to the transaction.

At step 205, node B may transmit the signed transaction E_(KB)(r_(t), t) and the signature SIGB back to node A.

At step 206, if SIGB is not successfully verified, node A may reject the transaction. If SIGB is successfully verified, node A may generate a range proof RP to prove to blockchain nodes if the value of PC(r_(t), t) and the value of PC(r_(y), y) are each within a valid range. For example, to have valid values of PC(r_(t), t), the transaction amount t may be within a valid range [0, 2^(n)−1]; and to have valid values of PC(r_(y), y), the change y may be within a valid range [0, 2^(n)−1]. In one embodiment, node A can use the block proof technique to generate the range proof RP related to (T, r_(t), t, Y, r_(y), y) for the blockchain nodes (e.g., consensus nodes) to verify at a later step whether the transaction amount t and the change y are within the valid range based on the range proof. The range proof may comprise, for example, Bulletproofs, Borromean ring signature, etc.

Further, node A may sign the transaction with user A's private key SK_(A) to generate a signature SIGA. Similarly, the signing may follow the Digital Signature Algorithm (DSA). In one embodiment, node A may sign ({PC(r_(a1), a₁), E_(KA)(r_(a1), a₁); PC(r_(a2), a₂), E_(KA)(r_(a2), a₂); PC(r_(ak), a_(k)), E_(KA)(r_(ak), a_(k))}; {PC(r_(y), y), E_(KA)(r_(y), y)}; {PC(r_(t), t), E_(KB)(r_(t), t)}; Y; T; r′; RP) with user A's private key to generate the signature SIGA, where {PC(r_(a1), a₁), E_(KA)(r_(a1), a₁); PC(r_(a2), a₂), E_(KA)(r_(a2), a₂); . . . PC(r_(ak), a_(k)), E_(KA)(r_(ak), a_(k))} represents the tapped assets A₁, A₂, A_(k) from account A for the transaction. {PC(r_(y), y), E_(KA)(r_(y), y)} represents the change that account A will receive from the transaction. {PC(r_(t), t), E_(KB)(r_(t), t)} represents the transferred asset that account B will receive from the transaction.

At step 207, node A may submit the transaction to the blockchain, causing the blockchain nodes to verify the transaction and determine whether to add the transaction to the blockchain. In one embodiment, node A may submit the transaction ({PC(r_(a1), a₁), E_(KA)(r_(a1), a₁); PC(r_(a2), a₂), E_(KA)(r_(a2), a₂); . . . PC(r_(ak), a_(k)), E_(KA)(r_(ak), a_(k))}; {PC(r_(y), y), E_(KA)(r_(y), y)}; {PC(r_(t), t), E_(KB)(r_(t), t)}; Y; T; r′; RP; SIGA; SIGB) to the blockchain via node 1 to execute the transaction. The transaction may comprise additional parameters or may not comprise all of the listed parameters. The transaction may be broadcast to one or more nodes (e.g., consensus nodes) in the blockchain for verification. If the verification succeeds, the transaction is added to the blockchain. If the verification fails, the transaction is rejected from adding to the blockchain.

At steps 208-213, the one or more nodes (e.g., consensus nodes) verify the signatures, range proof, and other information of the submitted transaction. If the verification fails, the nodes reject the transaction. If the verification succeeds, the nodes accept the transaction, update user A's account and user B's account separately.

In some embodiments, to execute the transaction, transaction information may be verified by various blockchain nodes. The transaction information may comprise transaction address TXID, signature(s), input, and output. TXID may comprise the hash of the transaction content. The signatures may comprise crypto-key signatures by the sender and recipient. The input may comprise an address of the sender's account in blockchain, one or more assets tapped from the sender's blockchain account for transaction, etc. The output may comprise an address of the recipient's account in blockchain, asset type(s) of the recipient asset(s), commitment value(s) of the recipient asset(s), etc. The input and output may comprise indexed information in a tabular form. In some embodiments, the value of NoteID value can be “the TXID+an index of the asset in the output.”

In some embodiments, the one or more nodes of the blockchain may verify the submitted transaction ({PC(r_(a1), a₁), E_(KA)(r_(a1), a₁); PC(r_(a2), a₂), E_(KA)(r_(a2), a₂); . . . PC(r_(ak), a_(k)), E_(KA)(r_(ak), a_(k))}; {PC(r_(y), y), E_(KA)(r_(y), y)}; {PC(r_(t), t), E_(KB)(r_(t), t)}; Y; T; r′; RP; SIGA; SIGB).

At step 208, the nodes may verify whether the transaction has been executed using an anti-double-spending mechanism or anti-replay-attack mechanism. If the transaction has been executed, the nodes may reject the transaction; otherwise, the method may proceed to step 209.

At step 209, the nodes may check the signatures SIGA and SIGB (for example, based on A's public key and B's public key respectively). If any of the signatures is incorrect, the nodes may reject the transaction; otherwise, the method may proceed to step 210.

At optional step 210, the nodes may verify if the asset types are consistent. For example, the nodes may verify if the asset types in the NoteType for A₁ to A_(k) are consistent with the asset type(s) of the transaction amount t. If any of the asset types is inconsistent, the nodes may reject the transaction; otherwise, the method may proceed to step 211. In some embodiments, the original asset type in the wallet may have been converted to another type based on an exchange rate, and this step may be skipped.

At step 211, the nodes may check the range proof RP to validate the value of PC(r_(t), t) and the value of PC(r_(y), y). In one embodiment, the nodes may check the range proof RP to verify whether the transaction amount t is no less than zero and the change y is no less than zero. If the verification fails, the nodes may reject the transaction; otherwise, the method may proceed to step 212.

At step 212, the nodes may check if the inputs and the outputs of the transaction are consistent. In one embodiment, r′ may correspond to asset value t′=a₁+a₂ . . . +a_(k)−t−y based on the homomorphic property, where r′=(r₁+r₂ . . . +r_(k))−r_(t)−r_(y). Since the input assets are a₁+a₂ . . . +a_(k) and the output is t+y, t′=0 when the input and output are consistent: a₁+a₂ . . . +a_(k)=t+y. Thus, the commitment value corresponding to r′ is PC(r′, t′)=r′×G+t′×H=r′G. Since r′=(r₁+r₂ . . . +r_(k))−r_(t)−r_(y), the nodes can determine if the inputs and outputs are equal by verifying if r′G is equal to PC₁+ . . . +PC_(k)−T−Y corresponding to (r₁+r₂ . . . +r_(k))−r_(t)−r_(y). If r′G is equal to PC₁+ . . . +PC_(k)−T−Y, the nodes may determine that the inputs and the outputs of the transaction are consistent and proceed to the next step; otherwise, the nodes may determine that the inputs and the outputs of the transaction are inconsistent and reject the transaction.

At step 213, the nodes may verify if node A has the asset(s) tapped for the transaction. In one embodiment, the nodes may perform this verification based on information stored in the blockchain, such as information corresponding to account A. The information may comprise previous transaction information of all assets. The nodes can thus determine if account A has the transacting asset for the transaction. If the determination is no, the nodes may reject the transaction; otherwise, the method may proceed to step 214.

At step 214, the nodes may update the account A and account B. For example, the nodes may remove the transacting asset of amount t from account A, and add the same to account B. Based on the homomorphic property, since Y=PC(r_(y), y) and node 1 knows r_(y) and can access the commitment value Y from the blockchain, node 1 can decrypt Y to obtain the asset value y and return the same to account A. Node 2 obtains at step 202 the random number r_(t) from node 1 and can obtain from the blockchain the commitment value T. Thus, node 2 can decrypt T to obtain the asset value t and add the same to account B.

In one example, after the update to account A and account B, account A receives the change y to the tapped assets A₁, A₂, . . . , A_(k) and receives its untapped assets A_(ak+1), . . . , A_(m), and account B receives the transaction amount t and receives its original assets B₁, B₂, . . . , B_(n). The assets in A's account and B's account are as follows:

For A's Account (account A), updated assets are denoted as:

(Y = PC(r_(y), y), E_(KA)(r_(y), y)) (A_(ak + 1) = PC(r_(ak + 1), a_(k + 1)), E_(KA)(r_(ak + 1), a_(k + 1))) (A_(ak + 2) = PC(r_(ak + 2), a_(k + 2)), E_(KA)(r_(ak + 2), a_(k + 2))) ⋯(A_(m) = PC(r_(am), a_(m)), E_(KA)(r_(am), a_(m)))

For B's Account (account B), updated assets are denoted as:

(B₁ = PC(r_(b 1), b₁), E_(KB)(r_(b 1), b₁)), (B₂ = PC(r_(b 2), b₂), E_(KB)(r_(b 2), b₂)), ⋯(B_(n) = PC(r_(bn), b_(n)), E_(KB)(r_(bn), b_(n))), (T = PC(r_(t), t), E_(KB)(r_(t), t))

Although this disclosure uses node A/user A and node B/user B to illustrate the sender and recipient respectively, the sender and the recipient can be the same node/user. For example, the change y of a transaction (total tapped assets in account A minus the transaction amount) may be sent back to the sender of the transaction. Thus, the various steps performed by node B as described herein may alternatively be performed by node A.

FIG. 3 illustrates a flowchart of an exemplary method 300 for information protection, according to various embodiments of the present disclosure. The method 300 may be implemented by one or more components (e.g., node A, node 1, a combination of node A and node 1) of the system 100 of FIG. 1. The method 300 may be implemented by a system or device (e.g., computer, server) comprising a processor and a non-transitory computer-readable storage medium (e.g., memory) storing instructions. The instructions, when executed by the processor, cause the system or device (e.g., the processor) to perform the method 300. The operations of method 300 presented below are intended to be illustrative. Depending on the implementation, the exemplary method 300 may include additional, fewer, or alternative steps performed in various orders or in parallel.

Block 301 comprises: committing a transaction amount t of a transaction with a first commitment scheme to obtain a transaction commitment value T, and committing a change y of the transaction with a second commitment scheme to obtain a change commitment value Y, the first commitment scheme comprising a transaction blinding factor r_(t), and the second commitment scheme comprising a change blinding factor r_(y). In some embodiments, the first commitment scheme comprises a Pedersen commitment based at least on the transaction blinding factor r_(t) and with the transaction amount t being a corresponding committed value. See, e.g., T=PC(r_(t), t). The second commitment scheme comprises a Pedersen commitment based at least on the change blinding factor r_(y) and with the change y being a corresponding committed value. See, e.g., Y=PC(r_(y), y).

Block 302 comprises: encrypting a first combination of the change blinding factor r_(y) and the change y with a first key KA.

Block 303 comprises: transmitting the transaction blinding factor r_(t), the transaction amount t, and the transaction commitment value T to a recipient node associated with a recipient of the transaction for the recipient node to verify the transaction. In some embodiments, transmitting the transaction blinding factor r_(t), the transaction amount t, and the transaction commitment value T to the recipient node associated with the recipient of the transaction for the recipient node to verify the transaction comprises: transmitting the transaction blinding factor r_(t), the transaction amount t, and the transaction commitment value T to the recipient node associated with the recipient of the transaction, causing the recipient node to verify if the transaction commitment value T is equal to the first commitment scheme committing the transaction amount t with the transaction blinding factor r_(t).

Block 304 comprises: in response to that the recipient node successfully verifies the transaction, obtaining an encrypted second combination of the transaction blinding factor r_(t) and the transaction amount t encrypted with a second key KB. In some embodiments, obtaining the encrypted second combination comprises receiving from the recipient node the encrypted second combination and a signature SIGB associated with the encrypted second combination and the transaction commitment value T.

Block 305 comprises: transmitting the encrypted first combination and the encrypted second combination to a plurality of nodes in a blockchain for the nodes in the blockchain to verify the transaction.

In some embodiments, the transaction amount t is tapped from one or more assets A₁, A₂, . . . , A_(k) of a sender of the transaction; each of the assets is associated with (1) a Pedersen commitment based at least on a blinding factor r_(ak) and a value of the each asset and (2) an encryption based at least on the blinding factor r_(ak) and the value of the each asset; and the change y is a difference between the transaction amount t and the tapped assets.

In some embodiments, before transmitting the encrypted first combination and the encrypted second combination to the plurality of nodes in the blockchain, the method further comprises: verifying the signature SIGB; and in response to successfully verifying the signature SIGB, generating a signature SIGA associated with the assets A₁, A₂, . . . , A_(k), the first combination, the second combination, the transaction commitment value T, the change commitment value Y, and a difference between a sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and a sum of the transaction blinding factor r_(t) and the change blinding factor r_(y). That is, the difference r′=(r₁+r₂ . . . +r_(k))−(r_(t)+r_(y)).

In some embodiments, transmitting the encrypted first combination and the encrypted second combination to the plurality of nodes in the blockchain comprises: transmitting the assets A₁, A₂, . . . , A_(k), the first combination, the second combination, the transaction commitment value T, the change commitment value Y, a difference between a sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and a sum of the transaction blinding factor r_(t) and the change blinding factor r_(y), the signature SIGA, and the signature SIGB to the plurality of nodes in the blockchain.

In some embodiments, transmitting the encrypted first combination and the encrypted second combination to the plurality of nodes in the blockchain for the nodes in the blockchain to verify the transaction comprises: transmitting the encrypted first combination and the encrypted second combination to the plurality of nodes in the blockchain, causing the nodes in the blockchain to, in response to successfully verifying the transaction, issue the transaction amount t to the recipient, eliminate the assets A₁, A₂, . . . , A_(k), and issue the change y to the sender.

FIG. 4 illustrates a flowchart of an exemplary method 400 for information protection, according to various embodiments of the present disclosure. The method 400 may be implemented by one or more components (e.g., node B, node 2, a combination of node B and node 2, etc.) of the system 100 of FIG. 1. The method 400 may be implemented by a system or device (e.g., computer, server) comprising a processor and a non-transitory computer-readable storage medium (e.g., memory) storing instructions. The instructions, when executed by the processor, cause the system or device (e.g., the processor) to perform the method 400. The operations of the method 400 presented below are intended to be illustrative. Depending on the implementation, the exemplary method 400 may include additional, fewer, or alternative steps performed in various orders or in parallel.

Block 401 comprises: obtaining a transaction blinding factor r_(t), a transaction amount t of a transaction, and a transaction commitment value T from a sender node associated with a sender of a transaction, wherein: the transaction amount t is committed with a first commitment scheme to obtain the transaction commitment value T, the first commitment scheme comprising the transaction blinding factor r_(t).

Block 402 comprises: verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T. In some embodiments, verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T comprises verifying if the obtained transaction commitment value T is equal to the first commitment scheme committing the obtained transaction amount t with the obtained transaction blinding factor r_(t).

Block 403 comprises: in response to successfully verifying the transaction, encrypting a second combination of the transaction blinding factor r_(t) and the transaction amount t with a second key KB.

Block 404 comprises: transmitting the encrypted second combination to the sender node. In some embodiments, before transmitting the encrypted second combination to the sender node, further comprising generating a signature SIGB associated with the encrypted second combination and the transaction commitment value T; and transmitting the encrypted second combination to the sender node comprises transmitting the encrypted second combination and the signature SIGB to the sender node.

As shown, the privacy for the transaction amount can be protected through various improvements of the computing technology. For example, the account structure comprise one or more fields, such as a first field associated with the Pedersen commitment of the asset value (e.g., the first field being PC(r_(a1), ai), with i being between 1 and m) and a second field associated with the random number for the Pedersen commitment and the asset value (e.g., the second field being E_(KA)(r_(a1), ai), with i being between 1 and m). The first field and second field are also used in the transaction steps and stored in blockchain.

For another example, a cryptographic key is used to encrypt the random number of each Pedersen commitment and the corresponding asset value. The cryptographic key for encryption/decryption is held by the account owner, thus the privacy of the asset values is protected from users without the cryptographic key. Further, the transaction including the encrypted random numbers and asset values is stored in the blockchain. This manner provides convenience for managing the random numbers, minimizes chances of loss and alteration of the random numbers and asset values, and promotes security based on the distributed and consistent blockchain storage.

The steps before submitting the transaction to blockchain may be treated as “off-chain” or “pre-transaction” behavior, since the encryption and decryption processes happen at client sides, while the blockchain stores the encrypted “asset value+corresponding random number” represented by the E( ) function. The Pedersen commitment may be similar to a safe with assets inside, and the “asset value+corresponding random number” is similar to the key to the safe. The encrypted key and its associated safe may be stored in the blockchain, which is temper-proof and anti-lost. Every time the user wants to expend the asset(s), the user can retrieve the safe and the encrypted key from blockchain and decrypt the key on the client side, so that the “pre-transaction” steps can be performed to assemble a new transaction that expends the asset(s).

As such, random numbers of Pedersen commitments can be conveniently managed, without the risk for corruption and without incurring additional key management burden. Thus, the transaction privacy can be thoroughly protected, and transaction amounts can be kept as secrets.

The techniques described herein are implemented by one or more special-purpose computing devices. The special-purpose computing devices may be desktop computer systems, server computer systems, portable computer systems, handheld devices, networking devices or any other device or combination of devices that incorporate hard-wired and/or program logic to implement the techniques. Computing device(s) are generally controlled and coordinated by operating system software. Conventional operating systems control and schedule computer processes for execution, perform memory management, provide file system, networking, I/O services, and provide a user interface functionality, such as a graphical user interface (“GUI”), among other things.

FIG. 5 is a block diagram that illustrates a computer system 500 upon which any of the embodiments described herein may be implemented. The system 500 may be implemented in any of the nodes described herein and configured to perform corresponding steps for information protection methods. The computer system 500 includes a bus 502 or other communication mechanism for communicating information, one or more hardware processor(s) 504 coupled with bus 502 for processing information. Hardware processor(s) 504 may be, for example, one or more general purpose microprocessors.

The computer system 500 also includes a main memory 506, such as a random access memory (RAM), cache and/or other dynamic storage devices, coupled to bus 502 for storing information and instructions to be executed by processor(s) 504. Main memory 506 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor(s) 504. Such instructions, when stored in storage media accessible to processor(s) 504, render computer system 500 into a special-purpose machine that is customized to perform the operations specified in the instructions. The computer system 500 further includes a read only memory (ROM) 508 or other static storage device coupled to bus 502 for storing static information and instructions for processor(s) 504. A storage device 510, such as a magnetic disk, optical disk, or USB thumb drive (Flash drive), etc., is provided and coupled to bus 502 for storing information and instructions.

The computer system 500 may implement the techniques described herein using customized hard-wired logic, one or more ASICs or FPGAs, firmware and/or program logic which in combination with the computer system causes or programs computer system 500 to be a special-purpose machine. According to one embodiment, the operations, methods, and processes described herein are performed by computer system 500 in response to processor(s) 504 executing one or more sequences of one or more instructions contained in main memory 506. Such instructions may be read into main memory 506 from another storage medium, such as storage device 510. Execution of the sequences of instructions contained in main memory 506 causes processor(s) 504 to perform the process steps described herein. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions.

The main memory 506, the ROM 508, and/or the storage device 510 may include non-transitory storage media. The term “non-transitory media,” and similar terms, as used herein refers to media that store data and/or instructions that cause a machine to operate in a specific fashion, the media excludes transitory signals. Such non-transitory media may comprise non-volatile media and/or volatile media. Non-volatile media includes, for example, optical or magnetic disks, such as storage device 510. Volatile media includes dynamic memory, such as main memory 506. Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid state drive, magnetic tape, or any other magnetic data storage medium, a CD-ROM, any other optical data storage medium, any physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, NVRAM, any other memory chip or cartridge, and networked versions of the same.

The computer system 500 also includes a network interface 518 coupled to bus 502. Network interface 518 provides a two-way data communication coupling to one or more network links that are connected to one or more local networks. For example, network interface 518 may be an integrated services digital network (ISDN) card, cable modem, satellite modem, or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, network interface 518 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN (or WAN component to communicated with a WAN). Wireless links may also be implemented. In any such implementation, network interface 518 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

The computer system 500 can send messages and receive data, including program code, through the network(s), network link and network interface 518. In the Internet example, a server might transmit a requested code for an application program through the Internet, the ISP, the local network and the network interface 518.

The received code may be executed by processor(s) 504 as it is received, and/or stored in storage device 510, or other non-volatile storage for later execution.

Each of the processes, methods, and algorithms described in the preceding sections may be embodied in, and fully or partially automated by, code modules executed by one or more computer systems or computer processors comprising computer hardware. The processes and algorithms may be implemented partially or wholly in application-specific circuitry.

The various features and processes described above may be used independently of one another, or may be combined in various ways. All possible combinations and sub-combinations are intended to fall within the scope of this disclosure. In addition, certain method or process blocks may be omitted in some implementations. The methods and processes described herein are also not limited to any particular sequence, and the blocks or states relating thereto can be performed in other sequences that are appropriate. For example, described blocks or states may be performed in an order other than that specifically disclosed, or multiple blocks or states may be combined in a single block or state. The exemplary blocks or states may be performed in serial, in parallel, or in some other manner. Blocks or states may be added to or removed from the disclosed exemplary embodiments. The exemplary systems and components described herein may be configured differently than described. For example, elements may be added to, removed from, or rearranged compared to the disclosed exemplary embodiments.

The various operations of exemplary methods described herein may be performed, at least partially, by an algorithm. The algorithm may be comprised in program codes or instructions stored in a memory (e.g., a non-transitory computer-readable storage medium described above). Such algorithm may comprise a machine learning algorithm. In some embodiments, a machine learning algorithm may not explicitly program computers to perform a function, but can learn from training data to make a predictions model that performs the function.

The various operations of exemplary methods described herein may be performed, at least partially, by one or more processors that are temporarily configured (e.g., by software) or permanently configured to perform the relevant operations. Whether temporarily or permanently configured, such processors may constitute processor-implemented engines that operate to perform one or more operations or functions described herein.

Similarly, the methods described herein may be at least partially processor-implemented, with a particular processor or processors being an example of hardware. For example, at least some of the operations of a method may be performed by one or more processors or processor-implemented engines. Moreover, the one or more processors may also operate to support performance of the relevant operations in a “cloud computing” environment or as a “software as a service” (SaaS). For example, at least some of the operations may be performed by a group of computers (as examples of machines including processors), with these operations being accessible via a network (e.g., the Internet) and via one or more appropriate interfaces (e.g., an Application Program Interface (API)).

The performance of certain of the operations may be distributed among the processors, not only residing within a single machine, but deployed across a number of machines. In some exemplary embodiments, the processors or processor-implemented engines may be located in a single geographic location (e.g., within a home environment, an office environment, or a server farm). In other exemplary embodiments, the processors or processor-implemented engines may be distributed across a number of geographic locations.

Throughout this specification, plural instances may implement components, operations, or structures described as a single instance. Although individual operations of one or more methods are illustrated and described as separate operations, one or more of the individual operations may be performed concurrently, and nothing requires that the operations be performed in the order illustrated. Structures and functionality presented as separate components in exemplary configurations may be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements fall within the scope of the subject matter herein.

Although an overview of the subject matter has been described with reference to specific exemplary embodiments, various modifications and changes may be made to these embodiments without departing from the broader scope of embodiments of the present disclosure. Such embodiments of the subject matter may be referred to herein, individually or collectively, by the term “invention” merely for convenience and without intending to voluntarily limit the scope of this application to any single disclosure or concept if more than one is, in fact, disclosed. The Detailed Description should not to be taken in a limiting sense, and the scope of various embodiments is defined only by the appended claims, along with the full range of equivalents to which such claims are entitled. 

1. A computer-implemented method for information protection, comprising: obtaining a transaction blinding factor r_(t), a transaction amount t of a transaction, and a transaction commitment value T from a sender node associated with a sender of a transaction, wherein: the transaction amount t is committed with a first commitment scheme to obtain the transaction commitment value T, the first commitment scheme comprising the transaction blinding factor r_(t); verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T; in response to successfully verifying the transaction, encrypting a second combination of the transaction blinding factor r_(t) and the transaction amount t with a second key KB; and transmitting the encrypted second combination to the sender node.
 2. The method of claim 1, wherein: verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T comprises verifying if the obtained transaction commitment value T is equal to the first commitment scheme committing the obtained transaction amount t with the obtained transaction blinding factor r_(t).
 3. The method of claim 1, wherein: before transmitting the encrypted second combination to the sender node, further comprising generating a signature SIGB associated with the encrypted second combination and the transaction commitment value T; and transmitting the encrypted second combination to the sender node comprises transmitting the encrypted second combination and the signature SIGB to the sender node.
 4. The method of claim 3, wherein: the transaction amount t is tapped from one or more assets A₁, A₂, . . . , A_(k) of the sender of the transaction; each of the assets is associated with (1) a Pedersen commitment based at least on a blinding factor r_(ak) and a value of the each asset and (2) an encryption based at least on the blinding factor r_(ak) and the value of the each asset; and a change y is a difference between the transaction amount t and the tapped assets.
 5. The method of claim 4, wherein transmitting the encrypted second combination and the signature SIGB to the sender node comprises: transmitting the encrypted second combination and the signature SIGB to the sender node for the sender node to verify the signature SIGB and to, in response to the sender node successfully verifying the signature SIGB, generate a signature SIGA associated with the assets A₁, A₂, . . . , A_(k), an encrypted first combination of a change blinding factor r_(y) and the change y encrypted with a first key KA, the encrypted second combination, the transaction commitment value T, a change commitment value Y committing the change y with a second commitment scheme, and a difference between a sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and a sum of the transaction blinding factor r_(t) and the change blinding factor r_(y)
 6. The method of claim 5, wherein transmitting the encrypted second combination and the signature SIGB to the sender node further comprises: transmitting the encrypted second combination and the signature SIGB to the sender node for the sender node to generate a blockchain transaction for adding to a blockchain, the blockchain transaction comprising: the assets A₁, A₂, . . . , A_(k), the encrypted first combination, the encrypted second combination, the transaction commitment value T, the change commitment value Y, the difference between the sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and the sum of the transaction blinding factor r_(t) and the change blinding factor r_(y), the signature SIGA, and the signature SIGB.
 7. The method of claim 1, wherein: the first commitment scheme comprises a Pedersen commitment based at least on the transaction blinding factor r_(t) and with the transaction amount t being a corresponding committed value.
 8. A non-transitory computer-readable storage medium storing instructions that, when executed by a processor, cause the processor to perform operations comprising: obtaining a transaction blinding factor r_(t), a transaction amount t of a transaction, and a transaction commitment value T from a sender node associated with a sender of a transaction, wherein: the transaction amount t is committed with a first commitment scheme to obtain the transaction commitment value T, the first commitment scheme comprising the transaction blinding factor r_(t); verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T; in response to successfully verifying the transaction, encrypting a second combination of the transaction blinding factor r_(t) and the transaction amount t with a second key KB; and transmitting the encrypted second combination to the sender node.
 9. The storage medium of claim 8, wherein: verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T comprises verifying if the obtained transaction commitment value T is equal to the first commitment scheme committing the obtained transaction amount t with the obtained transaction blinding factor r_(t).
 10. The storage medium of claim 8, wherein: before transmitting the encrypted second combination to the sender node, the operations further comprise generating a signature SIGB associated with the encrypted second combination and the transaction commitment value T; and transmitting the encrypted second combination to the sender node comprises transmitting the encrypted second combination and the signature SIGB to the sender node.
 11. The storage medium of claim 10, wherein: the transaction amount t is tapped from one or more assets A₁, A₂, . . . , A_(k) of the sender of the transaction; each of the assets is associated with (1) a Pedersen commitment based at least on a blinding factor r_(ak) and a value of the each asset and (2) an encryption based at least on the blinding factor r_(ak) and the value of the each asset; and a change y is a difference between the transaction amount t and the tapped assets.
 12. The storage medium of claim 11, wherein transmitting the encrypted second combination and the signature SIGB to the sender node comprises: transmitting the encrypted second combination and the signature SIGB to the sender node for the sender node to verify the signature SIGB and to, in response to the sender node successfully verifying the signature SIGB, generate a signature SIGA associated with the assets A₁, A₂, . . . , A_(k), an encrypted first combination of a change blinding factor r_(y) and the change y encrypted with a first key KA, the encrypted second combination, the transaction commitment value T, a change commitment value Y committing the change y with a second commitment scheme, and a difference between a sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and a sum of the transaction blinding factor r_(t) and the change blinding factor r_(y)
 13. The storage medium of claim 12, wherein transmitting the encrypted second combination and the signature SIGB to the sender node further comprises: transmitting the encrypted second combination and the signature SIGB to the sender node for the sender node to generate a blockchain transaction for adding to a blockchain, the blockchain transaction comprising: the assets A₁, A₂, . . . , A_(k), the encrypted first combination, the encrypted second combination, the transaction commitment value T, the change commitment value Y, the difference between the sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and the sum of the transaction blinding factor r_(t) and the change blinding factor r_(y), the signature SIGA, and the signature SIGB.
 14. The storage medium of claim 8, wherein: the first commitment scheme comprises a Pedersen commitment based at least on the transaction blinding factor r_(t) and with the transaction amount t being a corresponding committed value.
 15. A system for information protection, comprising a processor and a non-transitory computer-readable storage medium coupled to the processor, the storage medium storing instructions that, when executed by the processor, cause the system to perform operations comprising: obtaining a transaction blinding factor r_(t), a transaction amount t of a transaction, and a transaction commitment value T from a sender node associated with a sender of a transaction, wherein: the transaction amount t is committed with a first commitment scheme to obtain the transaction commitment value T, the first commitment scheme comprising the transaction blinding factor r_(t); verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T; in response to successfully verifying the transaction, encrypting a second combination of the transaction blinding factor r_(t) and the transaction amount t with a second key KB; and transmitting the encrypted second combination to the sender node.
 16. The system of claim 15, wherein: verifying the transaction based on the obtained transaction blinding factor r_(t), the obtained transaction amount t of a transaction, and the obtained transaction commitment value T comprises verifying if the obtained transaction commitment value T is equal to the first commitment scheme committing the obtained transaction amount t with the obtained transaction blinding factor r_(t).
 17. The system of claim 15, wherein: before transmitting the encrypted second combination to the sender node, the operations further comprise generating a signature SIGB associated with the encrypted second combination and the transaction commitment value T; and transmitting the encrypted second combination to the sender node comprises transmitting the encrypted second combination and the signature SIGB to the sender node.
 18. The system of claim 17, wherein: the transaction amount t is tapped from one or more assets A₁, A₂, . . . , A_(k) of the sender of the transaction; each of the assets is associated with (1) a Pedersen commitment based at least on a blinding factor r_(ak) and a value of the each asset and (2) an encryption based at least on the blinding factor r_(ak) and the value of the each asset; and a change y is a difference between the transaction amount t and the tapped assets.
 19. The system of claim 18, wherein transmitting the encrypted second combination and the signature SIGB to the sender node comprises: transmitting the encrypted second combination and the signature SIGB to the sender node for the sender node to verify the signature SIGB and to, in response to the sender node successfully verifying the signature SIGB, generate a signature SIGA associated with the assets A₁, A₂, . . . , A_(k), an encrypted first combination of a change blinding factor r_(y) and the change y encrypted with a first key KA, the encrypted second combination, the transaction commitment value T, a change commitment value Y committing the change y with a second commitment scheme, and a difference between a sum of blinding factors corresponding to the assets A₁, A₂, . . . , A_(k) and a sum of the transaction blinding factor r_(t) and the change blinding factor r_(y)
 20. The system of claim 15, wherein: the first commitment scheme comprises a Pedersen commitment based at least on the transaction blinding factor r_(t) and with the transaction amount t being a corresponding committed value. 